Yeah this is... Well, there really isn't a better word for it than awkward, no matter how many times she repeats it to herself. She's never going to live this down.

"It was, and I apologize." She gives Jim a guilty look and then takes a step back before sweeping her arms out as to the side as she bends at the waist in a bow. A bit formal, perhaps, but dreams does she need the extra few seconds to clear her mind enough to think. "I'm sorry. My name is Amelia Ronsam. I'm afraid a different Jim Kirk and I have a very... frictional relationship. I apologize for assuming that you were one in the same."

Cautiously, she offers her hand to him for a handshake. "I promise to be more careful in the future. Can I do something to make up for this slight?" It's not a great start to their relationship, but at least she's trying to make up for being a jerk to start?